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## Measures of Association and Impact

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**Measures of Associationand Impact**Michael O’Reilly, MD, MPH FETP Thailand Introductory Course**Objectives**• Describe and calculate measures of association such as risk ratio and odds ratio, and describe when use each • Describe and calculate measures of public health impact such as attributable risk percent and population attributable risk percent**Example for calculations: NHANES follow-up study**Original enrollment 1971 – 1975 Follow-up 1982 – 1984 • Complete follow-up on: - 189 diabetic men - 3151 nondiabetic men - 218 diabetic women - 3823 nondiabetic women Participants aged 40-77 years at enrollment Ref: Kleinman J, et al. Mortality among diabetics in a national sample. AJE 1988; 128:389-401**Risk**# new cases during a specified periodsize of population at start of period = "Attack rate"= Probability of getting disease= Risk of disease= Cumulative incidence= Incidence proportion**Example of Risk Calculation**• Deaths in diabetic men 100 deaths189 men at start of follow-up period 2. Deaths in nondiabetic men 811 deaths3151 men at start of follow-up period**Example of Risk Calculation**• Deaths in diabetic men 100 deaths189 men at start of follow-up period Risk = 100/189 = 52.9%**Example of Risk Calculation**2. Deaths in nondiabetic men 811 deaths3151 men at start of follow-up period Risk = 811/3151 = 25.7%**Person-Time Rate**# new cases during follow-up period # person-years of follow-up new cases during follow-up periodsum of the lengths of time each member of the population was at risk of disease = instantaneous incidence rate= Incidence density= "Person-time rate"**Denominator of P-T Rate**In a cohort (follow-up) study, follow each person until: • Onset of disease • Death • Loss to follow-up • End of study Add up the time each person was followed**P-T Rate – Example**Deaths in diabetic men If all enrolled in 1971, and if no deaths, and if all had been followed through 1984, denominator is: 189 × 13 = 2457 Person Years But some were enrolled 1972 - 1975, 100 died, & some were followed to 1982 or 1983. True denominator is: 1414.7 Person Years Rate = 100 / 1414.7 PY = 70.7 deaths / 1,000 PY (False rate 40.7 deaths/ 1,000 PY)**Odds**Odds in favor of an event = probability that event will occur probability that event will NOT occur Odds of disease = probability of disease 1 - probability of disease or, more simply, disease odds = # ill / # well**Example of an Odds Calculation**Deaths in diabetic men 100 deaths 189 men at start of follow-up period Probability of death = 100/189 = 52.9% Odds = probability of dying / probability of not dying = 0.529 / (1 - 0.529) = 0.529 / 0.471 = 1.1:1 Odds = # deaths / # survivors = 100 / 89 = 1.1:1**Example of an Odds Calculation**Odds of diabetes among men who died 100 deaths among diabetics 811 deaths among non-diabetics Prob. of diabetes = 100 / 911 = 0.110 = 11.0% ODDS = prob. of diabetes / prob. of non-diabetes = 0.110 / (1 - 0.110) = 0.110 / 0.890 = 1.23:1**"Every epidemiologic studycan be summarized in a 2-by-2**table." - H. Ory**Two-by-Two Tables**Ill Well Total Risk Exposed a b H1 a/H1 Not exp c d H2 c/H2 Total V1 V2 T or N**Mortality Among White Men, by Diabetic Status,NHANES**Follow-up Study, 1982-1984 Dead Alive Total Risk Diabetic 100 89 189 52.9% Not 811 2340 315125.7% diabetic Total 91124293340 27.3%**Measures of Association**Quantify the relationship between an"exposure" and outcome of interest Quantify the difference in occurrence of disease or death between two groups of people who differ on "exposure“ Types of measures:−Ratios: relative risk, rate ratio, odds ratio−Difference: attributable risk**Risk Ratio / Relative Risk**Risk in "exposed" groupRisk in "unexposed" group EXAMPLE:Relative risk of death among diabetic men vs. nondiabetic men RR: ?**Mortality Among White Men, by Diabetic Status,NHANES**Follow-up Study, 1982-1984 Dead Alive Total Risk Diabetic 100 89 189 52.9% Not 811 2340 315125.7% diabetic Total 91124293340 27.3%**Risk Ratio / Relative Risk**Risk in "exposed" groupRisk in "unexposed" group EXAMPLE:Relative risk of death among diabetic men vs. nondiabetic men RR: 100/189.257 811/3151 .529 = 2.1**Risk Ratio / Relative Risk**Risk in "exposed" groupRisk in "unexposed" group EXAMPLE:Relative risk of illness for those who ate food A vs. those who did not eat food A RR: ?**Risk Ratio / Relative Risk**EXAMPLE:Relative risk of illness for those who ate food A vs. those who did not eat food A RR: .80 .14 = 5.7**Questions about Risk Ratio**Risk in "exposed" group Risk in "unexposed" group • What does RR > 1 mean?• What does RR = 1 mean?• What does RR < 1 mean?**Comments about Risk Ratio**• The further away from 1, the stronger the association between exposure and disease • Can only calculate Risk Ratio from cohort study**Rate Ratio for P-T Rates**Person-time rate in "exposed" groupPT rate in "unexposed" group Example:Death rate ratio among diabetic men vs. nondiabetic men RR =100/1414.7 =70.7/1000 = 2.5 811/28,029.8 =28.9/1000**Comments about Rate Ratio**The further away from 1, the stronger the association between exposure and disease Can only calculate Rate Ratio from follow-up cohort study**Odds Ratio: General**If you are not using cohort study data, then relative risk is not obtainable Under certain circumstances, odds ratios are good estimates of the relative risk**Odds Ratio**FORMULA 1 (“Disease Odds Ratio”): Odds of disease/death in “exposed” groupOdds of dz/death in “unexposed” group FORMULA 2 (“Exposure Odds Ratio”): Odds of being "exposed" among casesOdds of "exposed" among non-cases**Disease Odds Ratio**Dead Alive Odds of disease Diabetic 100 89 100/89 Not 811 2340 811/2340 Total 9112429 Using formula 1: OR 100/89 = 100 x 2340 = 3.2 811/2340 89 x 811**Exposure Odds Ratio**Dead Alive Diabetic 100 89 Not 811 2340 Odds of 100/81189/2340 Exposure Using formula 2: OR 100/811 = 100 x 2340 = 3.2 89/2340 89 x 811**When Can the Odds Ratio be used to approximate the Relative**Risk? Ill Well Total Risk Exposed a b a + ba/a + b Not exp c d c + dc/c + d RR = a/a+b ≈ a/b ≈ ad c/c+d c/d bc For a rare disease, a <<< b, so a+b ≈ b c <<< d, so c+d ≈ d**Example of the “Rare Disease” Assumption?**Ill Well Total Risk Exposed a b a + ba/a + b Not exp c d c + dc/c + d RR = a/a+b ≈ a/b ≈ ad c/c+d c/d bc For a rare disease, a <<< b, so a+b ≈ b c <<< d, so c+d ≈ d